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Properties

Label 1008.3.eg
Level $1008$
Weight $3$
Character orbit 1008.eg
Rep. character $\chi_{1008}(229,\cdot)$
Character field $\Q(\zeta_{12})$
Dimension $1520$
Sturm bound $576$

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Defining parameters

Level: \( N \) \(=\) \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 1008.eg (of order \(12\) and degree \(4\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 1008 \)
Character field: \(\Q(\zeta_{12})\)
Sturm bound: \(576\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(1008, [\chi])\).

Total New Old
Modular forms 1552 1552 0
Cusp forms 1520 1520 0
Eisenstein series 32 32 0

Trace form

\( 1520 q - 4 q^{2} - 6 q^{3} - 4 q^{4} - 6 q^{5} - 16 q^{8} + O(q^{10}) \) \( 1520 q - 4 q^{2} - 6 q^{3} - 4 q^{4} - 6 q^{5} - 16 q^{8} - 12 q^{10} + 2 q^{11} - 6 q^{12} + 30 q^{14} - 16 q^{15} - 4 q^{16} - 24 q^{17} + 80 q^{18} - 12 q^{19} + 14 q^{21} - 4 q^{22} - 6 q^{24} - 12 q^{26} + 24 q^{28} - 4 q^{29} + 10 q^{30} + 356 q^{32} - 12 q^{33} - 24 q^{34} - 58 q^{35} - 76 q^{36} - 4 q^{37} - 6 q^{38} - 6 q^{40} + 378 q^{42} - 4 q^{43} + 62 q^{44} - 6 q^{45} + 12 q^{46} - 4 q^{49} + 12 q^{50} - 118 q^{51} - 6 q^{52} - 4 q^{53} - 90 q^{54} + 456 q^{56} + 2 q^{58} - 534 q^{60} + 384 q^{63} - 16 q^{64} - 8 q^{65} - 666 q^{66} - 4 q^{67} - 6 q^{68} - 54 q^{69} + 194 q^{70} + 98 q^{72} - 82 q^{74} - 6 q^{75} - 198 q^{77} + 38 q^{78} - 8 q^{79} - 12 q^{80} - 4 q^{81} + 12 q^{82} - 720 q^{83} - 1578 q^{84} - 54 q^{85} + 302 q^{86} + 2 q^{88} + 540 q^{90} + 188 q^{91} + 60 q^{92} + 70 q^{93} - 8 q^{95} - 6 q^{96} + 86 q^{98} + 154 q^{99} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{3}^{\mathrm{new}}(1008, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.